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      The singular values and vectors of low rank perturbations of large rectangular random matrices

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      Journal of Multivariate Analysis

      Elsevier BV

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          Most cited references 29

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          Singular value decomposition for genome-wide expression data processing and modeling.

          We describe the use of singular value decomposition in transforming genome-wide expression data from genes x arrays space to reduced diagonalized "eigengenes" x "eigenarrays" space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.
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            Calculating the Singular Values and Pseudo-Inverse of a Matrix

             G. Golub,  W. Kahan (1965)
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              Eigenvalues of large sample covariance matrices of spiked population models

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                Author and article information

                Journal
                Journal of Multivariate Analysis
                Journal of Multivariate Analysis
                Elsevier BV
                0047259X
                October 2012
                October 2012
                : 111
                :
                : 120-135
                Article
                10.1016/j.jmva.2012.04.019
                © 2012

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